Many practical applications, such as determination of future power demand, depend on predicting future environmental conditions, e.g., temperature, daylight and humidity. Because measurements of environmental conditions form non-stationary time series, their prediction for applications such as power generation and distribution, fuel prices, and the scheduling of the operation of heating, ventilation and air conditioning (HVAC) equipment is more complicated.
A number of time series prediction methods are based on an auto-regressive moving average (ARMA) model. The ARMA model, also known as the Box-Jenkins model, predicts future values from time series data Xt. The model includes an autoregressive (AR) part, and a moving average (MA) part. ARMA models are suitable for prediction of stationary time series, but do not perform well on non-stationary time series.
One method for predicting non-stationary data takes the difference of the time series as many times as necessary to make the resulting time series stationary. Such a model is also known as an integrated ARMA (ARIMA) model. However, if the seasonal and diurnal components are non-linear after the differencing, then the resulting time series can exhibit non-linear dependencies, which would preclude the use of low-order linear prediction models for the modeling.
The direct application of more advanced machine learning techniques, such as neural networks, wavelets, and support vector machines (SVM), to the prediction of time series data can often be inaccurate, despite their ability to model dynamic systems. This has been attributed to both numerical optimization difficulties, as well as to possible mismatches between the model and the physical process that generates the time series data.
Therefore, it is desired to predict accurately future conditions in non-stationary environments.